24 research outputs found
Localness of energy cascade in hydrodynamic turbulence, I. Smooth coarse-graining
We introduce a novel approach to scale-decomposition of the fluid kinetic
energy (or other quadratic integrals) into band-pass contributions from a
series of length-scales. Our decomposition is based on a multiscale
generalization of the ``Germano identity'' for smooth, graded filter kernels.
We employ this method to derive a budget equation that describes the transfers
of turbulent kinetic energy both in space and in scale. It is shown that the
inter-scale energy transfer is dominated by local triadic interactions,
assuming only the scaling properties expected in a turbulent inertial-range. We
derive rigorous upper bounds on the contributions of non-local triads,
extending the work of Eyink (2005) for low-pass filtering. We also propose a
physical explanation of the differing exponents for our rigorous upper bounds
and for the scaling predictions of Kraichnan (1966,1971). The faster decay
predicted by Kraichnan is argued to be the consequence of additional
cancellations in the signed contributions to transfer from non-local triads,
after averaging over space. This picture is supported by data from a
pseudospectral simulation of Navier-Stokes turbulence with phase-shift
dealiasing.Comment: 26 pages, 4 figure
Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-graining Approach
This is the final version of the article. Available from AMS via the DOI in this record.A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer rely on the assumption of statistical homogeneity, or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space, and is not restricted by those assumptions. This paper describes how the framework can be applied to ocean flows. Energy transfer between scales is not unique due to a gauge freedom. Here, it is argued that a Galilean invariant subfilter scale (SFS) flux is a suitable quantity to properly measure energy scale-transfer in the Ocean. It is shown that the SFS definition can yield answers that are qualitatively different from traditional measures that conflate spatial transport with the scale-transfer of energy. The paper presents geographic maps of the energy scale-transfer that are both local in space and allow quasi-spectral, or scale-by-scale, dynamics to be diagnosed. Utilizing a strongly eddying simulation of flow in the North Atlantic Ocean, it is found that an upscale energy transfer does not hold everywhere. Indeed certain regions, near the Gulf Stream and in the Equatorial Counter Current have a marked downscale transfer. Nevertheless, on average an upscale transfer is a reasonable mean description of the extra-tropical energy scale-transfer over regions of O(10^3) kilometers in size.Financial
support was provided by IGPPS at Los Alamos National Laboratory (LANL)
and NSF grant OCE-1259794. HA was also supported through DOE grants
de-sc0014318, de-na0001944, and the LANL LDRD program through project
number 20150568ER. MH was also supported through the HiLAT project of
the Regional and Global Climate Modeling program of the DOEâs Office of Science,
and GKV was also supported by NERC, the Marie Curie Foundation and
the Royal Society (Wolfson Foundation). This research used resources of the
National Energy Research Scientific Computing Center, a DOE Office of Science
User Facility supported by the Office of Science of the U.S. Department
of Energy under Contract No. DE-AC02-05CH11231
Localness of energy cascade in hydrodynamic turbulence, II. Sharp spectral filter
We investigate the scale-locality of subgrid-scale (SGS) energy flux and
inter-band energy transfers defined by the sharp spectral filter. We show by
rigorous bounds, physical arguments and numerical simulations that the spectral
SGS flux is dominated by local triadic interactions in an extended turbulent
inertial-range. Inter-band energy transfers are also shown to be dominated by
local triads if the spectral bands have constant width on a logarithmic scale.
We disprove in particular an alternative picture of ``local transfer by
nonlocal triads,'' with the advecting wavenumber mode at the energy peak.
Although such triads have the largest transfer rates of all {\it individual}
wavenumber triads, we show rigorously that, due to their restricted number,
they make an asymptotically negligible contribution to energy flux and
log-banded energy transfers at high wavenumbers in the inertial-range. We show
that it is only the aggregate effect of a geometrically increasing number of
local wavenumber triads which can sustain an energy cascade to small scales.
Furthermore, non-local triads are argued to contribute even less to the
space-average energy flux than is implied by our rigorous bounds, because of
additional cancellations from scale-decorrelation effects. We can thus recover
the -4/3 scaling of nonlocal contributions to spectral energy flux predicted by
Kraichnan's ALHDIA and TFM closures. We support our results with numerical data
from a pseudospectral simulation of isotropic turbulence with
phase-shift dealiasing. We conclude that the sharp spectral filter has a firm
theoretical basis for use in large-eddy simulation (LES) modeling of turbulent
flows.Comment: 42 pages, 9 figure
Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence
The effects of different filtering strategies on the statistical properties
of the resolved-to-sub-filter scale (SFS) energy transfer are analyzed in
forced homogeneous and isotropic turbulence. We carry out a priori analyses of
statistical characteristics of SFS energy transfer by filtering data obtained
from direct numerical simulations (DNS) with up to grid points as a
function of the filter cutoff scale. In order to quantify the dependence of
extreme events and anomalous scaling on the filter, we compare a sharp Fourier
Galerkin projector, a Gaussian filter and a novel class of Galerkin projectors
with non-sharp spectral filter profiles. Of interest is the importance of
Galilean invariance and we confirm that local SFS energy transfer displays
intermittency scaling in both skewness and flatness as a function of the cutoff
scale. Furthermore, we quantify the robustness of scaling as a function of the
filtering type
Energy Transfer and Spectra in Simulations of Two-dimensional Compressible Turbulence
We present results of high-resolution numerical simulations of compressible
2D turbulence forced at intermediate spatial scales with a solenoidal
white-in-time external acceleration. A case with an isothermal equation of
state, low energy injection rate, and turbulent Mach number
without energy condensate is studied in detail. Analysis of energy spectra and
fluxes shows that the classical dual-cascade picture familiar from the
incompressible case is substantially modified by compressibility effects. While
the small-scale direct enstrophy cascade remains largely intact, a large-scale
energy flux loop forms with the direct acoustic energy cascade compensating for
the inverse transfer of solenoidal kinetic energy. At small scales, the direct
enstrophy and acoustic energy cascades are fully decoupled at small Mach
numbers and hence the corresponding spectral energy slopes comply with
theoretical predictions, as expected. At large scales, dispersion of acoustic
waves on vortices softens the dilatational velocity spectrum, while the
pseudo-sound component of the potential energy associated with coherent
vortices steepens the potential energy spectrum.Comment: 10 pages, 6 figures. To appear in: Turbulence in Complex Conditions,
Proc. Euromech/Ercoftac Colloquium 589, ed. M. Gorokhovski, Springer, 201
Physical Processes in Star Formation
© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00693-8.Star formation is a complex multi-scale phenomenon that is of significant importance for astrophysics in general. Stars and star formation are key pillars in observational astronomy from local star forming regions in the Milky Way up to high-redshift galaxies. From a theoretical perspective, star formation and feedback processes (radiation, winds, and supernovae) play a pivotal role in advancing our understanding of the physical processes at work, both individually and of their interactions. In this review we will give an overview of the main processes that are important for the understanding of star formation. We start with an observationally motivated view on star formation from a global perspective and outline the general paradigm of the life-cycle of molecular clouds, in which star formation is the key process to close the cycle. After that we focus on the thermal and chemical aspects in star forming regions, discuss turbulence and magnetic fields as well as gravitational forces. Finally, we review the most important stellar feedback mechanisms.Peer reviewedFinal Accepted Versio
Joint downscale fluxes of energy and potential enstrophy in rotating stratified Boussinesq flows
We employ a coarse-graining approach to analyze non-linear cascades in Boussinesq flows using high-resolution simulation data. We derive budgets which resolve the evolution of energy and potential enstrophy simultaneously in space and in scale. We then use numerical simulations of Boussinesq flows, with forcing in the large scales, and fixed rotation and stable stratification along the vertical axis, to study the inter-scale flux of energy and potential enstrophy in three different regimes of stratification and rotation: i) strong rotation and moderate stratification, ii) moderate rotation and strong stratification, and iii) equally strong stratification and rotation. In all three cases, we observe constant fluxes of both global invariants, the mean energy and mean potential enstrophy, from large to small scales. The existence of constant potential enstrophy flux ranges provides the first direct empirical evidence in support of the notion of a cascade of potential enstrophy. The persistent forward cascade of the two invariants reflects a marked departure of these flows from two-dimensional turbulence
Global cascade of kinetic energy in the ocean and the atmospheric imprint
Here, we present an estimate for the ocean's global scale transfer of kinetic energy (KE), across scales from 10 to 40,000 km. Oceanic KE transfer between gyre scales and mesoscales is induced by the atmosphereâs Hadley, Ferrel, and polar cells, and the intertropical convergence zone induces an intense downscale KE transfer. Upscale transfer peaks at 300 gigawatts across mesoscales of 120 km in size, roughly one-third the energy input by winds into the oceanic general circulation. Nearly three quarters of this âcascadeâ occurs south of 15°S and penetrates almost the entire water column. The mesoscale cascade has a self-similar seasonal cycle with characteristic lag time of â27 days per octave of length scales; transfer across 50 km peaks in spring, while transfer across 500 km peaks in summer. KE of those mesoscales follows the same cycle but peaks â40 days after the peak cascade, suggesting that energy transferred across a scale is primarily deposited at a scale four times larger